Given that x2+5x-1=0 has 2 roots α and β, evaluate the following expressions.
(1) α2-αβ+β2
(2) (α-2β)(2α-β)
Evaluate the following expressions
2007-11-11 9:30 pm
回答 (1)
2007-11-11 9:41 pm
✔ 最佳答案
α + β = -5 and αβ = -1(1) α2-αβ+β2 = (α + β)^2 - 3αβ = (-5)^2 - 3(-1) = 25+3 = 28
(2) (α-2β)(2α-β) = 2α^2 + 2β^2 - 5αβ
= 2(α+β)^2 - 9αβ
= 2(-5)^2 - 9(-1)
= 50+9
= 59
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